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Trace theorems: critical cases and best constants


Authors: Michael Ruzhansky and Mitsuru Sugimoto
Journal: Proc. Amer. Math. Soc. 143 (2015), 227-237
MSC (2010): Primary 35B65, 35E15, 46E35, 35Q41, 42B37; Secondary 42B99, 42B35, 35S05, 35Q40
DOI: https://doi.org/10.1090/S0002-9939-2014-12207-6
Published electronically: August 28, 2014
MathSciNet review: 3272748
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Abstract: The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces and to give the asymptotics for the norms of the traces under dilations of the surface. We also discuss the best constants for them.


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Additional Information

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: m.ruzhansky@imperial.ac.uk

Mitsuru Sugimoto
Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
Email: sugimoto@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2014-12207-6
Received by editor(s): September 26, 2012
Received by editor(s) in revised form: March 20, 2013
Published electronically: August 28, 2014
Additional Notes: The first author was supported by the EPSRC Leadership Fellowship EP/G007233/1
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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